{
  "abstract": "We study the finite extensions of a number field generated by a single point on an elliptic curve. We construct geometrically non-isomorphic elliptic curves with complex multiplication that generate the same collection of extensions, giving a negative answer to a question of Mazur and Rubin. For torsion-generated fields, we prove that inclusion of the collections up to finitely many exceptions implies isogeny over the ground field, and in the non-CM case even isomorphism. When all geometric endomorphisms are defined over the ground field, we characterize equality of the torsion-generated collections by the existence, for every prime $p$, of an isogeny over the ground field of degree prime to $p$. This condition also implies equality of the full collections of fields generated by a single point.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07259",
  "author_total": 2,
  "authors": [
    {
      "name": "Minseok Kim"
    },
    {
      "name": "Myungjun Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c26pnhm33f799.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07259",
  "fulltext_url": null,
  "id": "c26pnhm33f799",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07259",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07259",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c26pnhm33f799.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.07259",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07259"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Fields Generated by a Single Point on Elliptic Curves",
  "title_text": "Fields Generated by a Single Point on Elliptic Curves",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:47Z",
  "url": "https://research.draconitic.com/paper/c26pnhm33f799",
  "venue": "arXiv",
  "versions": []
}